Finite Group Databasebeta

← #20244729

Subgroups — #20244729

Order 6016.

250 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094015C211yesmaximal, characteristic
2C2×#13093958C211yesmaximal, characteristic
3C2×#13093955C211yesmaximal, characteristic
4#15689022C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9#13094015—22no—
10#13094015—22no—
11C2×C4⋊Dic47—21no—
12C2×C4⋊Dic47—21no—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4—21no—
16C2×C4×Dic47C2211yescharacteristic
17#13093958—22no—
18#13093955—22no—
19C47⋊#95—21no—
20C22×C8×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47C2311yescharacteristic
26C22×Dic47—21no—
27C22×Dic47—21no—
28C22×Dic47D411yescharacteristic
29C22×Dic47D411yescharacteristic
30C2×C8×C47—21no—
31C2×C8×C47—21no—
32C2×C8×C47Q812yes—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47D412yes—
36C4⋊C4×C47Q812yes—
37C4⋊Dic47—24no—
38C4⋊Dic47—21no—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—42no—
42C4⋊Dic47D412yes—
43Dic47⋊C4—24no—
44C4×Dic47—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8Q812yes—
49C23×C47C2×D411yescharacteristic
50C2×C4×C47—22no—
51C2×C4×C47—22no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×Q811yescharacteristic
59C2×C4×C47C2×Q811yescharacteristic
60C2×C4×C47C2×Q811yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—22no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—21no—
69C2×Dic47—41no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47—41no—
74C8×C47—22no—
75C47⋊C8—22no—
76C22×C47#12011yescharacteristic
77C22×C47C22⋊Q811yescharacteristic
78C22×C47C4⋊Q811yescharacteristic
79C22×C47#13511yescharacteristic
80C22×C47#13511yescharacteristic
81C22×C47AGL(1,ℤ/8)11yescharacteristic
82C22×C47#13711yescharacteristic
83C4×C47—42no—
84C4×C47—42no—
85C4×C47C22⋊Q811yescharacteristic
86C4×C47C22⋊Q811yescharacteristic
87C4×C47C4⋊Q811yescharacteristic
88C4×C47C4⋊Q811yescharacteristic
89Dic47—41no—
90Dic47—42no—
91Dic47—41no—
92Dic47—81no—
93#2059—471nomaximal, Sylow
94C2×C47#39511yescharacteristic
95C2×C47#44911yescharacteristic
96C2×C47#45211yescharacteristic
97C2×C47#47811yescharacteristic
98C2×C47#47911yescharacteristic
99C2×C47#49911yescharacteristic
100C2×C47#50111yescharacteristic
101C2×#125—471no—
102C2×#107—471no—
103C2×#106—471no—
104#389—471no—
105#340—471no—
106#340D4711yescharacteristic
107#336—471no—
108C47#205911yescharacteristic, complemented, Sylow
109C22×C8—471no—
110C22×C8C2×D4711yescharacteristic
111#125—942no—
112#125—942no—
113C2×C4⋊C4—471no—
114C2×C4⋊C4—471no—
115C2×C4⋊C4—941no—
116C2×C4⋊C4—941no—
117C2×C4⋊C4—941no—
118C2×C4⋊C4C2×D4711yescharacteristic
119C2×C4⋊C4C2×D4711yescharacteristic
120C2×C42—471no—
121#107—942no—
122#106—942no—
123#95—941no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—471no—
127C22×C4—471no—
128C22×C4—941no—
129C22×C4—941no—
130C22×C4C22×D4711yescharacteristic
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—472no—
134C2×C8—941no—
135C2×C8—941no—
136C2×C8Dic9412yes—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—472no—
140C4⋊C4—944no—
141C4⋊C4—944no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C4⋊C4—1882no—
146C4⋊C4Dic9412yes—
147C4⋊C4D18812yes—
148C42—941no—
149C42—941no—
150C23D4×D4711yescharacteristic
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—941no—
158C2×C4—941no—
159C2×C4—942no—
160C2×C4—941no—
161C2×C4—941no—
162C2×C4—941no—
163C2×C4—941no—
164C2×C4—1881no—
165C2×C4—1881no—
166C2×C4—1881no—
167C2×C4—1881no—
168C2×C4—1881no—
169C2×C4C2×Dic9411yescharacteristic
170C2×C4C2×Dic9411yescharacteristic
171C2×C4C2×D18811yescharacteristic
172C2×C4D4×D4711yescharacteristic
173C2×C4#1062535211yescharacteristic
174C2×C4Q8×D4711yescharacteristic
175C8—22no—
176C8—942no—
177C22#1309399411yescharacteristic
178C22#1309400111yescharacteristic
179C22#1309402311yescharacteristic
180C22#1309404311yescharacteristic
181C22#1309404711yescharacteristic
182C22#1309405111yescharacteristic
183C22#1309405311yescharacteristic
184C4—42no—
185C4—42no—
186C4—3761no—
187C4—1881no—
188C4—1882no—
189C4—1881no—
190C4#1309400111yescharacteristic
191C4#1309400411yescharacteristic
192C4#1309402311yescharacteristic
193C4#1309402411yescharacteristic
194C2#1568904411yescharacteristic
195C2#1568927111yescharacteristic
196C2#1568928611yescharacteristic
197C2#1568942111yescharacteristic
198C2#1568943211yescharacteristic
199C2#1568952411yescharacteristic
200C2#1568953011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2059
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
108. C47#2059semidirect